Robust estimation based on the third-moment restriction of the error terms for the Box-Cox transformation model: An estimator consistent under heteroscedasticity

The Box-Cox (1964) transformation model is widely used in various fields of econometrics and statistics. Generally, the maximum likelihood estimator under the normality assumption (BC MLE) is used. However, the BC MLE is not consistent under heteroscedasticity, even if the “small sigma†assumption is satisfied.　Here I propose a new robust estimator of the Box-Cox transformation model. The estimator is based on only the first- and third-moment restrictions of the error terms, and it is consistent even under heteroscedasticity. Moreover, it can be easily calculated by the least-squares and scanning methods. The asymptotic distribution of the proposed estimator was obtained, and the results of Monte Carlo experiments are presented.